Question

A portfolio is comprised of equal weights of two stocks labeled Stock X and Stock Y. The covariance between Stock X and Stock Y is 0.10. The standard deviation of Stock X is 0.50, and the standard deviation of Stock Y is 0.50. Which of the following comes closest to the correlation coefficient between Stock X and Stock Y? O a. 0.40 b. 0.60 c. 0.00 O d. 0.50 o e. 1.00

Answer 1

Given that, the proportion of each stock X and stock Y are equal in the portfolio.

                                                Stock X                                 Stock Y

Weights 0.5                                       0.5

Standard Deviation 0.5                                      0.5

Covariance between stock X and stock Y is 0.1

The formula for calculation of correlation coefficient is:

                                Rxy       =      COV xy/ (σx x σy)

Where R xy = Correlation Coefficient

           COV xy = Covarience between X and Y

             σx                     = standarad deviation of X

             σy                      = standard deviation of Y

Applying the formula

            R xy      =    (0.1) / (0.5 x 0.5)

                        =     0.1 / 0.25

            R xy    =     0.40

Therefore, the correlation coefficient between X and Y is 0.40

So the answer is Option a,